# Inquiry regarding thermal resistor noise

In the simplest form, how could thermal resistor noise be described? I've looked up online but just found the calculation part.

Imagine an ordinary gas, like air, inside a room. If the room is perfectly sealed and the air is completely still, we can say that the average motion of all the gas molecules is zero. However, each individual molecule is taking a random path all over, colliding with the walls of the room and other molecules. The only way to get rid of this random motion of each molecule is to cool the gas to absolute zero temperature.

If you had a sufficiently sensitive microphone, you'd hear those molecules hitting the microphone. But there are so many molecules hitting the microphone all the time that what you hear is noise.

The same thing happens in electronics, but instead of gas molecules, it's electric charges (in metals, electrons) that are moving around. When electric charges move, that's a current. And by Ohm's law, when there's a current through some resistance, there's also a voltage.

So with a sufficiently sensitive instrument, we can detect the individual electrons moving through the resistor as a result of random thermal motion.

The power of this noise is a function of temperature. As the resistor heats up, the electrons move around more, so there's more noise.

For practical calculation at room temperature, the noise power can be calculated in dBm by:

$$-174 + 10 \log_{10}(\Delta f)$$

Here, $\Delta f$ is the bandwidth of interest, in hertz. For example, single sideband is typically within a 4kHz channel, so at room temperature the noise power within this channel is:

$$-174 + 10 \log_{10}(4000\:\mathrm{Hz}) = -138\:\mathrm{dBm}$$

More precisely, noise power in watts can be calculated by:

$$k_B T \Delta f$$

Where $k_B$ is Boltzmann's constant in joules per kelvin, and the temperature $T$ is in kelvin.

Note that these calculations of power assume that the noise is generated by some source impedance (say, a 50Ω antenna), and is going into an equal impedance. This is often the case in RF engineering and so works well because we can avoid introducing a resistance term in the equations. When this is not the case, it can be more convenient to calculate the RMS noise voltage, which is:

$$\sqrt{ 4 k_B T R \Delta f }$$

Likewise the RMS noise current is

$$\sqrt{ 4 k_B T\Delta f \over R}$$

I am a complete novice, so it does not necessarily mean that what I found on is something I understand, especially in terms of application to amateur radio - I would like to figure out how to apply some of the reduction techniques:

From a set of lecture notes from a college class: "Thermal noise is produced by the motion of free electrons in a resistance due to temperature. It is generated even when the resistance is not connected to a circuit but is due to the random fluctuations in charge at either end of the resistance. Thermal noise is often called Johnson noise.

The noise power in thermal noise is constant per unit of bandwidth across the usable electronic spectrum. Because of this, it is a form of white noise. The maximum noise power available from a thermal noise source is given by the equation: Pn = kTB

On pp. 155-191, noise reduction techniques are discussed in detail; the main techniques include:

• Capacitors
• Varistors
• Suppressors
• Screening tehcniques
• Grounds, Shields, and Connecting Wires
• Filters

From wikipedia, there is a bit more background:

"Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. The generic, statistical physical derivation of this noise is called the fluctuation-dissipation theorem, where generalized impedance or generalized susceptibility is used to characterize the medium.

Thermal noise in an ideal resistor is approximately white, meaning that the power spectral density is nearly constant throughout the frequency spectrum (however see the section below on extremely high frequencies). When limited to a finite bandwidth, thermal noise has a nearly Gaussian amplitude distribution.1" ....... Thermal noise is distinct from shot noise, which consists of additional current fluctuations that occur when a voltage is applied and a macroscopic current starts to flow. For the general case, the above definition applies to charge carriers in any type of conducting medium (e.g. ions in an electrolyte), not just resistors. It can be modeled by a voltage source representing the noise of the non-ideal resistor in series with an ideal noise free resistor. ......